My research spans problems in cosmology, astrophysics, particle physics and condensed matter physics. In cosmology, my work has focused on issues at the interface between fundamental physics (particle physics and string theory), general relativity and astrophysics. The mechanisms for driving inflationary expansion in the early universe, the connection between inflation and elementary particles, and the observational consequences of inflation are subjects of longstanding interest. Over the last decade, my research has turned to a radical alternative to standard big bang/inflationary cosmology known as the "cyclic universe," in which the big bang is not the beginning of space and time but rather a bounce from a pre-existing phase of contraction into a phase of expansion accompanied by the creation of hot matter and radiation; the key events that smoothed and flattened the universe occur before the last bang; dark energy plays a role in smoothing and flattening the universe prior to the next contraction phase and next big bang; and the entire cycle repeats every trillion years or so.
The cyclic universe is motivated, in part, by the discovery that the universe is entering an epoch of accelerated expansion. Since the mid-1990s, my group has been playing a leading role establishing the experimental case for accelerated expansion and exploring the possibility that the acceleration is driven by a dynamical energy component with negative pressure, called ``quintessence." More recently, the effort has turned to combining the idea of a slowly time-varying cosmological constant and a cyclic universe can naturally explain the small, positive value observed today. Other topics which our group continues to purse are alternative models of dark matter, such as strongly self-interacting elementary particles; modifcations of Einstein gravity; time-variation of fundamental constants; and the implications of inflationary and cyclic cosmology for primordial gravitational waves and non-gaussian perturbations in the early universe.
In condensed matter physics, a long-term focus has been on quasicrystals, novel solids with quasiperiodic atomic order which exhibit symmetries forbidden to ordinary crystals (such as five-fold symmetry in two-dimensions and icosahedral symmetry in three-dimensions). We have proposed a new paradigm for the structure of quaiscrystals, known as the "quasi-unit cell" picture, in which atomic configuration can be decomposed into a single repeating cluster which can overlap its neighbors by sharing atoms. The picture has been tested by comparing predictions with the imaging and physical measurements of known quasicrystals. We are currently investigating whether the quasi-unit cell picture suggests simple mechanisms to explain why they form and how they grow.
An intriguing question is whether quasicrystals can form naturally. The issue is important for condensed matter physics because it provides insights into how easy and common it is for quasicrystals to form and because it may reveal new quasicrystallines solids not yet observed in the laboratory. For geology, the discovery of natural quasicrystals would open new directions in mineralogy, raising questions about where and how these exotic solids form. Recently, a promising candidate for a natural candidate was discovered by a collaboration including our group. The goals are now to understand its origin and search for more examples.
Independently, we are applying the geometric concepts to construct photonic quasicrystals -- heterostructuresaimed at trapping, redirecting and guiding light. We have designed structures composed of two dielectric materials arranged in a quasiperiodic pattern, constructed macroscopic models based on these designed, , tested them using microwaves, and measured their scattering and light-trapping properties. The promising results have led us to work on improving he design and miniaturizing the structures for optical applications. Recently, we have extended this study to a new class of disordered structures, known as "hyperuniform;" although the structures are isotropic and disordered, they exhibit surprising diffraction and band gap properties that make them optimal for some photonic applications. The study suggests that hyperuniform structures may have interesting elastic, electronic and phononic properties, as well, and may be relevant to a variety of biological and physical phenomena.
- J.-L. Lehners and P. Steinhardt, "Dark Energy and the Return of the Phoenix Universe," Phys. Rev. D 79,: 063503 (2009).
- L. Bindi, P. Steinhardt, N. Yao and P. Lu, "Natural Quasicrystals," Science 324, 1306 (2009).
- J-L. Lehners and P. Steinhardt, "Intuitive understanding of non-gaussianity in ekpyrotic and cyclic models," Phys. Rev. D78: 02356 (2009).
- M. Florescu, S.Torquato, and P. Steinhardt, "Designer materials with large complete bandgaps," PNAS 106, 20658 (2009).
- P. Steinhardt and N. Turok, "Why the cosmological consant is small and positive," Science 312, 1180 (20060.
- W. Man, M. Megens, P. Chaikin, and P. Steinhardt, "Experimental measurement of the photonic properties of icoshaedral quasicrystals," Nature 496, 993 (2005).
- P. Steinhardt and N. Turok, "A cyclic model of the universe," Science, 296, 1436 (2002).
- D.N. Spergel and P.J. Steinhardt, "Observational evidence for self-interacting cold dark matter," Phys. Rev. Lett. 84, 3760 (2000),